Also the number of transversals of a cyclic latin square of order 2n+1 and the number of orthomorphisms of the cyclic group of order 2n+1. - Ian M. Wanless (wanless(AT)maths.ox.ac.uk), Oct 07 2001

Also the number of complete mappings of a cyclic group of order 2n+1; also (2n+1) times the number of "standard" complete mappings of cyclic group of order 2n+1. - Jieh Hsiang, D.Frank Hsu and Yuh Pyng Shieh (arping(AT)turing.csie.ntu.edu.tw), May 08 2002

Suppose n is odd and let b(n)=a((n-1)/2). Then b(n) is odd; if n>3 and n is not 1 mod 3 then b(n) is divisible by 3n; b(n)=-2n mod n^2 in n is prime; b(n) is divisible by n^2 if n is composite; b(n) is asymptotically in between 3.2^n and 0.62^n n!. [Cavenagh, Wanless], [McKay, McLeod, Wanless], [Stones, Wanless] - Ian Wanless, Jul 30 2010